# Zeroes of Sine and Cosine

## Theorem

Let $x \in \R$.

### Zeroes of Cosine

$\cos x = 0$ if and only if $x = \paren {n + \dfrac 1 2} \pi$ for some $n \in \Z$.

### Zeroes of Sine

$\sin x = 0$, if and only if $x = n \pi$ for some $n \in \Z$.